Prep the pan and oven: Heat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or lightly grease each cup.
Make the cream cheese filling: In a medium bowl, beat softened cream cheese, powdered sugar, vanilla, and a pinch of salt until smooth and creamy.
Set aside. If it’s too loose, chill it while you make the batter.
Mix dry ingredients: In a large bowl, whisk flour, granulated sugar, brown sugar, baking soda, baking powder, salt, cinnamon, nutmeg, and ginger until evenly combined and lump-free.
Mix wet ingredients: In another bowl or large measuring cup, whisk pumpkin purée, eggs, oil, milk, and vanilla until smooth.
Combine batter: Pour the wet mixture into the dry ingredients. Gently fold with a spatula just until the flour disappears. Do not overmix.
A few small lumps are fine.
Fill the muffin cups: Add about 2 tablespoons of batter to each cup. Spoon about 1 heaping teaspoon of the cream cheese mixture on top. Cover with another tablespoon or so of batter, filling cups about 3/4 full.
Swirl (optional but pretty): Add a small dab of cream cheese on top and swirl gently with a toothpick for a marbled look.
Sprinkle with turbinado sugar if using.
Bake: Bake for 18–22 minutes, until the tops spring back lightly and a toothpick inserted near the edge (not through the cream cheese center) comes out clean. The cream cheese will remain soft.
Cool: Let muffins cool in the pan for 5 minutes, then transfer to a wire rack. Cool at least 15 more minutes before eating so the center sets.